Probability Workshop – TT2017

Speaker: Jeffrey Rosenthal, University of TorontoTitle: Conditions for Convergence of Adaptive MCMC AlgorithmsAbstract: Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis Algorithm and the Gibbs Sampler, are an extremely popular method of approximately sampling from complicated probability distributions. Adaptive MCMC attempts to automatically modify the algorithm while it runs, to improve its performance on the fly. However, such modifications can destroy the convergence properties necessary for the algorithm to be valid. In this talk, we first illustrate MCMC algorithms using simple graphical Java applets. We then discuss adaptive MCMC, and present examples and theorems concerning its convergence and efficiency. We close with some recent results which provide more easily verifiable sufficient conditions for convergence.